Curious....what's the diameter of the washer head?GRK cabinet screws. They have them at both Lowes and Home Depot. Either 1" or 1.25". Put them about every 5" or so.
https://www.lowes.com/pd/GRK-8-x-1-...erior-Exterior-Wood-Screws-100-Count/50303177
It's not noted on the product page.